The Cosmic Perspective (8th Edition)
8th Edition
ISBN: 9780134059068
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
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Chapter S1, Problem 24EAP
Choose the best answer to each of the following Explain your reasoning with one or more complete sentences.
24. Jupiter is brightest when it is (a) at opposition. (b) at conjunction. (c) closest to the Sun in its orbit.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter S1 Solutions
The Cosmic Perspective (8th Edition)
Ch. S1 - Prob. 1VSCCh. S1 - Use the following questions to check your...Ch. S1 - Use the following questions to check your...Ch. S1 - Use the following questions to check your...Ch. S1 - Use the following questions to check your...Ch. S1 - Prob. 6VSCCh. S1 - Prob. 7VSCCh. S1 - Explain the differences between a (a) sidereal day...Ch. S1 - Prob. 2EAPCh. S1 - Prob. 3EAP
Ch. S1 - Prob. 4EAPCh. S1 - Prob. 5EAPCh. S1 - Prob. 6EAPCh. S1 - What are declination and right ascension? How are...Ch. S1 - 8. How and why do the Sun’s celestial coordinates...Ch. S1 - 9. Suppose you ire at the North Pole. Where is the...Ch. S1 - 10. Describe the Sun’s path through the local sky...Ch. S1 - 11. What is special about the tropics of Cancer...Ch. S1 - 2. Briefly describe how you can use the Sun or...Ch. S1 - Does It Make Sense? Decide whether the statement...Ch. S1 - Does It Make Sense?
Decide whether the statement...Ch. S1 - Does It Make Sense?
Decide whether the statement...Ch. S1 - Does It Make Sense?
Decide whether the statement...Ch. S1 - Does It Make Sense?
Decide whether the statement...Ch. S1 - Does It Make Sense?
Decide whether the statement...Ch. S1 - Does It Make Sense?
Decide whether the statement...Ch. S1 - Does It Make Sense?
Decide whether the statement...Ch. S1 - Does It Make Sense?
Decide whether the statement...Ch. S1 - Does It Make Sense? Decide whether the statement...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Choose the best answer to each of the following...Ch. S1 - Transits and the Geocentric Universe. Ancient...Ch. S1 - Geometry and Science. As discussed in Mathematical...Ch. S1 - Find Your Way Home. Roles: Scribe (takes notes on...Ch. S1 - Prob. 36EAPCh. S1 - Prob. 37EAPCh. S1 - Prob. 38EAPCh. S1 - Prob. 39EAPCh. S1 - Sydney Sky. Repeat Problem 39 for the local sky in...Ch. S1 - Prob. 41EAPCh. S1 - Prob. 42EAPCh. S1 - Be sure to show all calculations clearly and state...Ch. S1 - Be sure to show all calculations clearly and state...Ch. S1 - Be sure to show all calculations clearly and state...Ch. S1 - Prob. 46EAPCh. S1 - Be sure to show all calculations clearly and state...Ch. S1 - Be sure to show all calculations clearly and state...Ch. S1 - Be sure to show all calculations clearly and state...Ch. S1 - Be sure to show all calculations clearly and state...Ch. S1 - Be sure to show all calculations clearly and state...Ch. S1 - Northern Chauvinism. Why is the writing on maps...Ch. S1 - Celestial Navigation. Briefly discuss how you...Ch. S1 - Prob. 54EAPCh. S1 - Prob. 55EAPCh. S1 - Global Positioning System. Learn more about the...
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